It is not under FCA rules because it is, in essence, a graduate tax with a lifetime limit on the amount you pay. Despite being called a loan, it is not a loan in any real sense. A real loan would appear on the student's credit history, the repayments would not depend on earnings and the loan would not be written off after a fixed period.
No minor receives a student loan. A student is 18 when they start university. They may be a minor when they apply (although most are not), but they are definitely not minors when they start to receive the loan.
There is a clear complaints process for student loans. Ultimately, students can complain to the Financial Ombudsman for mortgage-style loans, the Parliamentary and Health Service Ombudsman for other loans (or a different ombudsman if the student is in Scotland, Wales or Northern Ireland).
FCA lenders do not have to offer fixed rates on all loans.
There is nothing to stop a student taking a loan from a commercial lender to cover their tuition and maintenance. However, as the student has no income, a commercial lender will require a guarantee from the parents, the amount lent will depend on parental income (contrary to what you say), they will require repayment regardless of the student's earnings, the loan will not be written off until it is repaid, the interest rate may be fixed but it will be much higher than the government charges and, overall, the terms will be much worse than those on offer from SLC. But, given the amounts involved, most lenders will simply refuse to lend that much to a student. That is why there is no competition.
RPI is used because this is a tax and the government wants to reduce public subsidies for higher education.
The SLC is clearly not for profit, so I'm not clear what point you are making. It loses around £300M per year.
Yes, a lot of loans will never be paid off but, given that the government has to pump billions of pounds into the scheme every year, I wouldn't say that means higher earners are subsidising the less well off. It means the government is subsidising the less well off.